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International Journal of Mathematics and Mathematical Sciences
Volume 15, Issue 3, Pages 455-463
http://dx.doi.org/10.1155/S0161171292000619

On the lower semi-continuity of the set valued metric projection

Department of Mathematical Sciences, Umm Al-Qura University, Makkah, Saudi Arabia

Received 28 November 1988; Revised 30 July 1991

Copyright © 1992 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The lower semi-continuity of best approximation operators from Banach lattices on to closed ideals is investigated. Also the existence of best approximation to sub-function modules of function modules is proved. The order intersection properties of cells are studied and used to prove the above results.